Monads on multiprojective spaces and associated vector bundles

In this paper we establish the existence of monads on multiprojective spaces X = P a 1 × P a 1 × P a 2 × P a 2 × ⋯ × P a n × P a n . As the existence of monads is nontrivial, we first set out to establish their existence on X . Once the monad on X exists the next natural question is whether the coho...

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Bibliographic Details
Published in:Manuscripta mathematica 2023-11, Vol.172 (3-4), p.1187-1200
Main Author: Maingi, Damian M.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Homology
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Summary:In this paper we establish the existence of monads on multiprojective spaces X = P a 1 × P a 1 × P a 2 × P a 2 × ⋯ × P a n × P a n . As the existence of monads is nontrivial, we first set out to establish their existence on X . Once the monad on X exists the next natural question is whether the cohomology vector bundle associated to these monads are simple or not. We study the kernel vector bundles and the cohomology bundle associated to monads on X and prove their stability and simplicity respectively.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-022-01449-0